Energy and Work.

Energy and work are so related that many people take them to mean the same thing. But they are not. Or are they really the same? 🤔

Have you ever tried to kick a ball with your leg? Well, if you have, that is some work done right there. And, do you know what makes that work done possible? Yeah, you guessed right. It is energy.

Work and energy are different in some ways and similar in other ways. So, to get a clear picture of how they relate, let’s get a hang on what they are individually about.

What is Work?

In ordinary terms, work is simply the force applied on an object or body through a distance. Like, when you open a door with your hand, you are using the force from your hand to move the door over a distance (horizontal distance). Or when you use your hand to lift an object from the ground, your hand is applying force to lift the object over a distance (vertical distance).

In scientific terms, work is the force that is used and is sufficient enough to move an object against resistance. In other words, for work to be done on an object, force applied on the object must overcome a resistance (opposing force).

For example, for you to lift an object up from the floor, the force you apply to lift it up must overcome the gravitational force holding it down. It is when the object has been lifted up that work is done.

Another example is when you try to push a block across a surface. For work to be done, the force you apply to move the block must overcome the opposing frictional force.

In physics, work is not just merely force applied on an object through a distance. it is more than that. Just because a force is applied to a body or object doesn’t mean a work is done.

According to the work-energy theorem, work is only done on an object when its kinetic energy changes.  That is, when a force moves an object from point A to B, the work is done on the object if the kinetic energy of the object changes. And this kinetic energy change is only possible when some components of the applied force are in the direction or opposite direction to the motion of the object.

For example, when you are lifting an object up, work is done because your force is pulling the object up, in the opposite direction to the gravitational force pulling it down.

NOTE: When you are holding an object up, you are not doing any work. The work had already been done while you were lifting the object up.

So, in physics, Work can, explicitly, be defined as the measure of energy change that occurs on an object, as a result of a force applied in the direction or opposite direction to the motion of the object.

Work would happen when a force is applied. And this force is possible only when there is energy.

In essence, without energy, no work can be done. So, what is energy?

Key Points: Work can simply be defined as the force applied to an object over a distance. The kinetic-energy theory defines work done as the change in the kinetic energy of a body.

What is Energy?

The most common definition is: energy is the capacity or ability for a body to do work. Yeah, it simply means that for work to be done, energy must be available. For example, for you to push a door with your hand, you must use energy. That is, you need energy in your body to provide that force to push the door.

Get a comprehensive look at energy here.

Key Points: Energy is the capability of a body or object to perform work.

The Work-Energy Theorem

The relationship between work done and energy is very well explained by the work-energy theorem. The work-energy theorem states that the work done on an object is equal to the change in the kinetic energy of that object.

Now, let’s prove this theorem.

First off, kinetic energy is simply the energy possessed by a body in motion. That is, when an object moves, it exhibits kinetic energy. It is represented by KE = mv2/2, where m is the mass of the object (in Kg) and v is the velocity (in m/s).

Now, consider an object with an initial velocity, u. If a force, F is applied to the object, the object is displaced through a distance, s, and undergoes an acceleration, a. Thus, a new velocity, v, is created. Putting this in form of an equation of motion, we have: v2 = u2 + 2as ——- (1)

The equation (1) can be re-written as: v2 – u2 = 2as ——– (2)

Multiply the equation (2) by mass, m

That will give mv2 – mu2 = 2mas ——– (3)

Dividing all through by 2, we get: mv2/2 – mu2/2 = mas ——– (4)

Work done = Force * distance = F * s = ma *s = mas

Here, Force, F is the net force.

Replacing ‘mas’ in equation 4 with work done will give: mv2/2 – mu2/2 = Work done ——– (5)

From equation 5, mv2/2 – mu2/2 means the change in the kinetic energy of the object.

And this change in kinetic energy of the object is equal to work done by the Force.

So, Work done = Change in Kinetic Energy (proved)

Key Points: Work-Energy Theorem: Work Done = Change in Kinetic energy

Why Work and Energy are Measured in Joules?

Work and energy have the same standard unit which is Joules. And this is because work done is perceived to be energy in use. Also, the work-energy theorem has proven work done to be equal to change in kinetic energy. Thereby, the same units

Are Work and Energy Really the Same?

Energy is pretty broad as it comes in different types. But, there is just one type of work.

Energy is what leads to work while work is a result of the availability of energy.

Energy and work have more like a cause and effect relationship. Energy is what causes work to be done while work is the effect of what the energy can do.

So, is work and energy really the same? I don’t think so. But are they related? Of course, they are.

2 thoughts on “How Energy and Work Are Related?

  1. Doc says:

    Thanks, it’s all coming back to me! Though, I think it would really help to explicitly define “a” in the equation “v^2 = u^2 + 2as”. I assume you meant “accelerated at a rate a” when you were defining v and s towards the beginning, right? Also, numbering the equations as they’re introduced would be helpful for reading comprehension if they’re going to be referred to as “first” or “second” later on. Just a couple suggestions for how to make things as clear as possible for jerks like me who can barely remember what F = ma means. I don’t know, maybe I’m just being spoiled and picky.

    1. Moshood says:

      Great suggestions, Doc. My interest is in making my write-ups easy for users to comprehend. Thanks for helping out, on this front.

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